It’s been a while since I last posted fractal images…
In retrospect, it was obvious the Mandelbrot set would rotate into a circle. After all, I knew from the start that there was no point rotating it about the real axis, so why I didn’t make that tiny logical leap to axial symmetry I have no idea. Still, it was fun finding out the hard way.
Click for animation – Warning! 18MB file size
Francis James Franklin (Alina Meridon) 
I don’t know much about this. Could you explain?
Mathematically: The simplest and most traditional form (that I use) of the problem goes:
1. Choose a constant number. Let’s call it C.
2. Take another number – start with the number zero. Let’s call it Z.
3. Multiply the number Z by itself, and add the specified constant C.
4. Repeat Step 3 until Z is bigger than two.
It’s a very simple sequence. Now, obviously, if C is big, then there will be few if any repetitions. If C is very small, then there will be lots of repetitions. Where it gets interesting is if you let C be a complex number with real and imaginary parts – represented in the image by horizontal and vertical respectively, with zero somewhere in the middle of that largest black region – then sometime the repetitions go on forever. And that black figure represents all the values of C for which that happens.
On a personal level: I have all my life (well, from mid-teens, I guess) had a passion for programming computers, and whenever I have learned a new language or a new operating system I have set myself the challenge of learning how to create the graphical image of the Mandelbrot set.